Robust Appointment Scheduling

Health care providers are under tremendous pressure to reduce costs and increase quality of their services. It has long been recognized that well-designed appointment systems have the potential to improve utilization of expensive personnel and medical equipment and to reduce waiting times for patients. In a widely influential survey on outpatient scheduling, Cayirli and Veral (2003) concluded that the "biggest challenge for future research will be to develop easy-to-use heuristics." We analyze the appointment scheduling problem from a robust-optimization perspective, and we establish the existence of a closed-form optimal solution--arguably the simplest and best `heuristic' possible. In case the order of patients is changeable, the robust optimization approach yields a novel formulation of the appointment scheduling problem as that of minimizing a concave function over a supermodular polyhedron. We devise the first constant-factor approximation algorithm for this case.

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